Laser beam irradiation method that includes determining a thickness of semiconductor prior to crystallizing

ABSTRACT

A laser beam irradiation method that achieves uniform crystallization, even if a film thickness of an a-Si film or the like fluctuates, is provided. The present invention provides a laser beam irradiation method in which a non-single crystal semiconductor film is formed on a substrate having an insulating surface and a laser beam having a wavelength longer than 350 nm is irradiated to the non-single crystal semiconductor film, thus crystallizing the non-single crystal silicon film. The non-single crystal semiconductor film has a film thickness distribution within the surface of the substrate, and a differential coefficient of a laser beam absorptivity with respect to the film thickness of the non-single crystal semiconductor film is positive.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a method of irradiating a laser beam,and in particular, to a method of irradiating a laser beam that is usedin forming an active layer of a thin film transistor or the like.

2. Description of the Related Art

Techniques of crystallizing a semiconductor film formed on an insulatingsubstrate such as glass and techniques of increasing crystallinitythereof by using laser annealing have been researched widely in recentyears. As a material for the semiconductor film, silicon (Si) is used inmany cases. A technique of crystallizing a semiconductor film by using alaser beam, thus obtaining a crystalline semiconductor film, and amethod of irradiating a laser beam to a semiconductor film, thusincreasing crystallinity, are referred to as “laser crystallization”within this specification. Further, films that undergo laser irradiationduring laser crystallization are referred to as “irradiation films”.

Compared to synthetic quartz glass substrates, which are often usedconventionally, glass substrates have the advantages of low cost, goodworkability, and the ease with which large area substrates can be made.This is the reason that the aforementioned research is being carriedout. Further, the reason that lasers are preferably used incrystallization is that the glass substrate melting point is low, and itis necessary to reduce the processing temperature to a temperature equalto or less than 600° C. Lasers can impart high energy only to asemiconductor film without causing the substrate temperature to increasevery much. Further, a throughput is considerably high compared to aheating means that uses an electric heating furnace.

Crystalline semiconductor films formed by laser beam irradiation havehigh mobility, and therefore thin film transistors (TFTs) are formedusing the crystalline semiconductor films. For example, the crystallinesemiconductor films are utilized in an active matrix liquid crystaldisplay device, or the like, in which TFTs used in a pixel portion, orTFTs used in the pixel portion and a driver circuit, are formed on oneglass substrate.

A method of using a pulse oscillation laser (pulse laser) and a methodof using a continuous wave laser (CW laser) exist as laser light sourcesused in laser crystallization. Excimer lasers such as XeCl lasers, andhigher harmonics of solid lasers such as Nd:YAG lasers, Nd:YVO₄ lasers,and Nd:YLF lasers may be used as laser light sources for the formermethod, and gas lasers such as Ar lasers, and higher harmonics of solidCW lasers such as Nd:YAG lasers and Nd:YVO₄ lasers may be used as laserlight sources for the latter method.

Amorphous silicon films (a-Si) and polysilicon films (poly-Si) aresemiconductor films that can undergo laser crystallization, and thecrystallinity of these non-single crystal semiconductor films isincreased by performing laser crystallization.

However, if an a-Si film is formed by plasma CVD on a large areasubstrate, there is a problem in that the film thickness of the formeda-Si film varies according to location within the substrate surface dueto the plasma distribution during film formation, the reaction gasoutflow distribution, the temperature distribution of heated substrate,and the like, and a film thickness distribution thus develops. Further,if a poly-Si film is formed from a-Si, film thickness variations thatoccur during film formation of the a-Si film still remain.

For example, if an a-Si film is formed on a 600 mm×720 mm glasssubstrate by using plasma CVD, variations of ±5% of the a-Si filmthickness develop within the substrate surface.

If a state exists in which the film thickness of the non-single crystalsemiconductor film has dispersions depending on locations within thesubstrate surface, the energy necessary for crystallization in locationsat which the film thickness has increased becomes relatively larger, andthe energy necessary for crystallization in locations at which the filmthickness has decreased becomes relatively smaller.

It is extremely difficult to control laser beam energy by the size ofthe film in thickness, and therefore only a fixed energy can be impartedto the irradiation film if laser crystallization is performed by using,for example, a pulse laser such as an excimer laser. The degree ofcrystallization thus differs depending on location within the substratesurface, and the grain size of the polycrystalline semiconductor filmobtained becomes non-uniform in locations within the substrate surface.A problem therefore exists in that variations develop in thecharacteristics of TFTs formed on a large area substrate.

On the other hand, solid pulse lasers and solid CW lasers using solidlaser media (hereinafter both are referred to together as solid lasers)are maintenance-free, have stable output, and are superior to excimerlasers in mass production because it is possible to have higherrepetitive oscillation when using a solid laser as a pulse laser thanwhen using an excimer laser.

A technique of laser crystallization for forming a polycrystallinesilicon film having a large grain size of several tens of micrometers ona glass substrate by using a CW Nd:YVO₄ laser with LD excitation hasbeen developed recently. It is possible to manufacture TFTs havingelectron mobility equal to or greater than 600 cm²/Vs by using thistechnique. Forming an LSI containing a CPU on a glass substrate, toproduce a “sheet computer”, is moving closer and closer to realization.

However, there are not many types of solid lasers at present, and almostall available solid lasers have an oscillation wavelength (fundamentalwave) in the red color region or the infrared region. Semiconductorfilms absorb almost no light in the red color region or the infraredregion, and therefore the second harmonic (2ω), the third harmonic (3ω),or a higher harmonic corresponding to a wavelength in the range of thevisible light region to the ultraviolet light region is used when asolid laser is utilized during laser crystallization. However, theenergy conversion efficiency with respect to the fundamental wave ishighest with the second harmonic, and therefore it is advantageous fromthe perspective of an energy to use the second harmonic.

The wavelength of the second harmonic of a solid laser is mainly in thevisible light region on the long wavelength side greater than 350 nm.The wavelengths of the second harmonic of typical solid lasers are shownas follows: Nd:YAG laser: 532 nm; Nd:YVO₄ laser: 532 nm; Nd:YLF laser:527 nm (or 524 nm); Ti:sapphire laser: 345 to 550 nm (variablewavelength); and Alexandrite laser: 350 to 410 nm (variable wavelength).

The skin depth to the semiconductor film is deep when using the secondharmonic of a solid laser for laser crystallization compared to anexcimer laser beam or the like having a wavelength in the ultravioletlight region, and therefore repetitive reflection develops within thesemiconductor thin film, and there is interference between the reflectedbeam and the incident beam. The optical characteristics of the laserbeam with respect to the irradiation film (reflectivity, transmissivity,and absorptivity) periodically fluctuate due to the film thickness ofthe semiconductor film due to the effect of the interference.

Refer to FIGS. 1A and 1B. FIG. 1A is a diagram showing absorptionspectra of a-Si films formed on a glass substrate. Reference numeral 101denotes an adsorption spectrum when the a-Si film thickness is 30 nm,reference numeral 102 denotes an adsorption spectrum when the a-Si filmthickness is 50 nm, reference numeral 103 denotes an adsorption spectrumwhen the a-Si film thickness is 70 nm, reference numeral 104 denotes anadsorption spectrum when the a-Si film thickness is 90 nm, and referencenumeral 105 denotes an adsorption spectrum when the a-Si film thicknessis 110 nm. Further, FIG. 1B is a diagram showing absorption spectra ofpoly-Si films formed on a glass substrate. Reference numeral 111 denotesan adsorption spectrum when the poly-Si film thickness is 30 nm,reference numeral 112 denotes an adsorption spectrum when the poly-Sifilm thickness is 50 nm, reference numeral 113 denotes an adsorptionspectrum when the poly-Si film thickness is 70 nm, reference numeral 114denotes an adsorption spectrum when the poly-Si film thickness is 90 nm,and reference numeral 115 denotes an adsorption spectrum when thepoly-Si film thickness is 110 nm.

It can be seen that the light absorption spectra are dependent upon theirradiation film thickness in the visible light region, on the longwavelength side greater than 350 nm. If laser crystallization isperformed using a laser beam that possesses a wavelength in thiswavelength region, then the energy imparted to the semiconductor filmvaries due to the film thickness of the semiconductor film itself, evenif the laser beam energy is fixed.

Refer to FIGS. 2A and 2B. FIG. 2A is a diagram showing a film thicknessdependence for light absorptivity by an a-Si film at a wavelength of 308nm (reference numeral 201), and a film thickness dependence for lightabsorptivity by an a-Si film at a wavelength of 532 nm (referencenumeral 202). FIG. 2B is a diagram showing a film thickness dependencefor light absorptivity by a poly-Si film at a wavelength of 308 nm(reference numeral 211), and a film thickness dependence for lightabsorptivity by a poly-Si film at a wavelength of 532 nm (referencenumeral 212).

As can be understood from FIGS. 2A and 2B, the skin depth to thesemiconductor film is shallow in laser crystallization methods that useexcimer lasers, such as an XeCl laser, because the laser beam wavelengthis in the ultraviolet light region. Therefore there is no dependence ofthe light absorptivity on the irradiation film thickness, and there areno fluctuations of the energy imparted to the semiconductor film bylaser irradiation due to the film thickness of the semiconductor filmitself. On the other hand, if the film thickness of the a-Si film or thelike fluctuates in laser crystallization methods that use the secondharmonic of a solid laser, then the light absorptivity corresponding tothe fluctuations is attenuated periodically and exponentially, and theenergy imparted to the semiconductor film also fluctuates in a similarmanner. It is therefore difficult to achieve uniform crystallization.

Laser crystallization methods that use the second harmonic of aconventional solid laser have been found to have more disadvantages inthis point than laser crystallization methods that use an excimer laserbeam.

The inventors of the present invention noticed that the dependence ofthe light absorptivity on the film thickness that can be seen for thesecond harmonic of a solid laser is rather effective against the problemof variations in crystallinity within the substrate surface caused byvariations in the film thickness of the irradiation film within thesubstrate surface. In other words, by limiting the film thickness of theirradiation film, the energy absorbed becomes relatively larger atlocations within the substrate surface when the film thickness of theirradiation film increases, and the energy absorbed becomes relativelysmaller at locations within the substrate surface when the filmthickness of the irradiation film decreases in laser crystallizationusing the second harmonic of a solid laser, and it is considered thatcrystallization can proceed to the same degree. It is thus expected thatvariations in the TFT characteristics within the substrate surface canbe reduced.

SUMMARY OF THE INVENTION

An object of the present invention is to provide a laser beamirradiation method, and a method of manufacturing a thin filmtransistor, which are capable of reducing non-uniformity in the degreeof crystallization of a polycrystalline semiconductor film formed byusing laser crystallization, and reducing variations in TFTcharacteristics, caused by variations in the film thickness of anon-single crystal semiconductor film within a surface of a large areasubstrate having an insulating surface when manufacturing the TFTs onthe substrate.

After conducting extensive studies on how to resolve the aforementionedproblem, and also considering experimental results, the inventors of thepresent invention have finally completed this invention. In order tosolve the aforementioned problem, a non-single crystal semiconductorfilm, formed having a specific target film thickness, undergoes lasercrystallization using a laser beam having a long wavelength greater than350 nm in the method of manufacturing a semiconductor device of thepresent invention.

According to the present invention, there is provided a laser beamirradiation method, comprising:

-   -   forming a non-single crystal semiconductor film over a substrate        having an insulating surface; and    -   irradiating a laser beam having a wavelength greater than 350 nm        to the non-single crystal semiconductor film to crystallize the        non-single crystal semiconductor film,

wherein:

-   -   the non-single crystal semiconductor film has a film thickness        distribution within its surface; and    -   a differential coefficient of an absorptivity of the laser beam        with respect to the film thickness of the non-single crystal        semiconductor film is positive.

The laser beam irradiation method according to the present inventioncomprises:

-   -   forming a non-single crystal semiconductor film on a substrate        having an insulating surface; and    -   irradiating a laser beam having a wavelength greater than 350 nm        to the non-single crystal semiconductor film to crystallize the        non-single crystal semiconductor film,

wherein:

-   -   the non-single crystal semiconductor film has a film thickness        distribution within its surface; and    -   the film thickness of the non-single crystal semiconductor film        during irradiation of the laser beam is determined by a        refractive index of the wavelength of the laser beam.

Also, according to the present invention, there is provided a method ofmanufacturing a thin film transistor, comprising:

-   -   forming a non-single crystal semiconductor film on a substrate        having an insulating surface; and    -   irradiating a laser beam having a wavelength greater than 350 nm        to the non-single crystal semiconductor film to crystallize the        non-single crystal semiconductor film,

wherein:

-   -   the non-single crystal semiconductor film has a film thickness        distribution within its surface; and    -   a differential coefficient of an absorptivity of the laser beam        with respect to the film thickness of the non-single crystal        semiconductor film is positive.

The method of manufacturing a thin film transistor according to thepresent invention, comprises:

-   -   forming a non-single crystal semiconductor film on a substrate        having an insulating surface; and    -   irradiating a laser beam having a wavelength greater than 350 nm        to the non-single crystal semiconductor film to crystallize the        non-single crystal semiconductor film,

wherein:

-   -   the non-single crystal semiconductor film has a film thickness        distribution within its surface; and    -   a center film thickness of the non-single crystal semiconductor        film in the laser beam irradiation is determined by a refractive        index of the wavelength of the laser beam.

BRIEF DESCRIPTION OF THE DRAWINGS

In the accompanying drawings:

FIGS. 1A and 1B show absorption spectra with respect to a wavelength ofa laser beam irradiated onto a-Si films and poly-Si films formed on aglass substrate;

FIGS. 2A and 2B show a film thickness dependence for light absorptivityby an a-Si film at a wavelength of 308 nm (reference numeral 201), and afilm thickness dependence for light absorptivity by an a-Si film at awavelength of 532 nm (reference numeral 202); and a film thicknessdependence for light absorptivity by a poly-Si film at a wavelength of308 nm (reference numeral 211), and a film thickness dependence forlight absorptivity by a poly-Si film at a wavelength of 532 nm,respectively (reference numeral 212);

FIGS. 3A and 3B show: an absorptivity, A(t), of light (532 nm) in ana-Si film found by computer simulation performed based on an index ofrefractive index (n) and an extinction constant (k) obtained from anellipsometer; a derivative dA(t)/dt of the light absorptivity A(t); andactual measured values of the absorptivity of light having a wavelengthof 532 nm when the a-Si film thickness is changed; and

FIGS. 4A and 4B show: an absorptivity, A(t), of light (532 nm) in apoly-Si film found by computer simulation performed based on an index ofrefractive index (n) and an extinction constant (k), obtained from anellipsometer; a derivative dA(t)/dt of the light absorptivity A(t); andactual measured values of the absorptivity of light having a wavelengthof 532 nm when the poly-Si film thickness is changed.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

A laser crystallization method is discussed in which the film thicknessof an irradiation film is set before laser crystallization so thatvariations in the degree of crystallization within a substrate surfaceafter performing laser crystallization are reduced for cases ofperforming laser crystallization over the entire substrate surface byusing the second harmonic (532 nm) of a CW Nd:YVO₄ laser to crystallizean amorphous silicon (a-Si) film formed on a glass substrate having aninsulating film. Variations in the film thickness of the a-Si filmdepending on locations within the substrate surface, and a dependence onthe a-Si film thickness of the absorptivity of 532 nm light, areinvestigated in advance, before film formation processing of the a-Sifilm.

The irradiation film is taken as an a-Si film formed by plasma chemicalvapor deposition (CVD). Further, the absorptivity of 532 nm light by ana-Si film substrate is taken as A(t) in this embodiment mode, where thea-Si film thickness is t.

First, variations in film thickness of the a-Si film formed by plasmaCVD are investigated, along with the dependence of 532 nm lightabsorptivity on the a-Si film thickness.

An a-Si film may be formed on a dummy substrate having the same size asthe actual substrate, for example, in investigating the variations inthe film thickness of the a-Si film, and the film thickness withinsubstrate surface of the dummy substrate may be measured at severalpoints by using a spectral ellipsometer.

Film thickness variations of approximately ±5% develop within thesubstrate surface when an a-Si film is formed on a 600 mm×720 mmsubstrate by using plasma CVD, for example. Thus, if the target filmthickness when forming the a-Si film is taken as t, film thicknessvariations develop within the substrate surface with a maximum filmthickness equal to 1.05 t, and a minimum film thickness equal to 0.95 t.

In order to investigate the a-Si film thickness dependence on theabsorptivity of 532 nm light, actual measurements of the absorptionspectrum may be made by using a spectral photometer, for example, onsubstrates on which an a-Si film is formed in advance, and the filmthickness of the a-Si film is to be clarified. Data showing thedependence of 532 nm light absorptivity upon a-Si film thickness can beobtained, provided that absorption spectrum measurements are made underseveral a-Si film thickness conditions.

Alternatively, the index of refraction of an a-Si film at 532 nm may befound by using a spectral ellipsometer or the like, and the lightabsorptivity A(t) may be found by running a computer simulation.Computer simulations are useful in finding a continuous lightabsorptivity dependence on the film thickness, without requiring a lotof effort.

Refer here to FIGS. 3A and 3B. Reference numeral 301 in FIG. 3A showsthe 532 nm light absorptivity A(t) found by a computer simulationperformed based on an index of refractive index (n) and an extinctionconstant (k) obtained from a spectral ellipsometer. Reference numeral302 denotes a derivative dA(t)/dt of the light absorptivity A(t) denotedby 301, and reference numeral 303 denotes actual measured values of the532 nm light absorptivity taken while varying the a-Si film thickness.Note that, for convenience of computation, the difference among thevariations in the light absorptivity with respect to the film thicknessmay be found as a substitute for the derivative of the lightabsorptivity A(t).

By comparing the actual measured values 303 with the simulation 301, itcan be seen that, although there is a small difference with the valuesof the derivative of the light absorptivity A(t), the values of the a-Sifilm thickness that denote the maximum value and the minimum value ofthe 532 nm light absorptivity have relatively good agreement.

If the derivative of the light absorptivity is found from the simulationresults of the light absorptivity at 532 nm by the a-Si film, and a-Sifilm thickness ranges in which dA(t)/dt>0 are selected, then a rangefrom 28 nm to 58 nm, a range from 86 nm to 115 nm, a range from 144 nmto 173 nm, and the like are found. Variations in the degree ofcrystallization due to film thickness variations can be reduced in aself-alignment manner, provided that the film thickness of the a-Si filmis within these ranges. This can be clearly understood by referring toFIG. 3B in which the graph of a region from 20 nm to 90 nm of FIG. 3A isblown up.

The a-Si film formed on the glass substrate at a target film thicknessof t possesses film thickness variations within the substrate surface,with the maximum film thickness equal to 1.05 t and the minimum filmthickness equal to 0.95 t. Therefore the film thickness t may beselected so that dA(t)/dt>0 is always true, even if the film thicknessfluctuates from 0.95 t to 1.05 t, in order to reduce variations in thedegree of crystallization, due to film thickness variations over theentire substrate surface, in a self-alignment manner.

Further, dA(t)/dt>0 expresses mathematically a state in which A(t)increases monotonically from the minimum value to the maximum value. Theperiodicity of the values of t showing maximum values and minimum valuesof A(t) may therefore be found in order to obtain a range for t at whichvariations in the degree of crystallization due to film thicknessvariations are reduced in a self-alignment manner. A method therefor isexplained below.

A light intensity distribution I(z) in a depth direction (z direction)of the semiconductor film for cases in which the semiconductor film isirradiated by laser light follows Lanbert's Law, expressed byI(z)=I(0)·(1−R)·exp(−αz), where I(O) denotes irradiation lightintensity, R denotes light reflectivity, and α denotes a lightabsorptivity coefficient.

The light absorptivity of a semiconductor film with respect to laserlight having a longer wavelength than 350 nm is attenuated periodicallyand exponentially in accordance with film thickness. The (1−R) termwithin respective I(z) terms described above contributes to periodicfluctuations, and the exp(−αz) term contributes to exponentialattenuation. Periodic fluctuation in the light reflectivity R becomes acause of periodic fluctuations in A(t) as shown directly in FIGS. 2A and2B, FIGS. 3A and 3B, and FIGS. 4A and 4B, and the a-Si film thicknessshowing maximum and minimum values of light absorptivity can easily befound by computing the minimum and maximum values of reflectivity.

If the reflectivity R(t) is considered for a case in which light is madeincident from a medium 0 (index of refraction n0) on a parallel planefilm (corresponding to the semiconductor film, film thickness t, indexof refraction n1) on a substrate (index of refraction n2), then valuesof t at which R(t) is a maximum value or a minimum value are determinedby the magnitude of relationship between n0, n1, and n2.

If laser wavelength is expressed by λ, and m is taken as a naturalnumber, then for a case (A) in which n2>n1>n0, or n2<n1<n0, there is nophase shift at the two film interfaces, and therefore an increasingreflectivity condition exists. R(t) takes on a minimum value whenn1×t=(2m+1)×λ/4, and takes on a maximum value when n1×t=2m×λ/4. For acase (B) in which n2>n1<n0, or n2<n1>n0, there is a phase shift at thetwo film interfaces. R(t) therefore takes on opposite values: a maximumvalue when n1×t=(2m+1)×λ/4, and a minimum value when n1×t=2m×λ/4.

The relationship between the indexes of refraction n2, n1, and n0normally satisfies the case (B) above for semiconductor films formed onglass substrates. For example, in the case of a single layer a-Si film,the index of refraction n2 of the glass substrate in the visible lightregion (300 nm to 800 nm) is approximately 1.5, and the index ofrefraction nil of the a-Si film is equal to or greater than 3.5 at awavelength region equal to or greater than 350 nm. A single layer filmis used, and therefore n0=1 (air).

The film thickness dependence of the light absorptivity fluctuatesperiodically in accordance with (1−R), and therefore A(t) takes on aminimum value when n1×t=(2m−1)×λ/4, and A(t) takes on a maximum valuewhen n1×t=2m×λ/4. A range of t at which dA(t)/dt>0 can thus be expressedby the following equation, using the laser wavelength λ and the index ofrefraction of the semiconductor film n1:

(2m−1)λ/4nl<t<2mλ/4nl (where m=1, 2, 3, . . . )

It can thus be seen from the above method that the ranges of the targetfilm thickness of an a-Si film capable of reducing variations in thedegree of crystallization, due to variations in the film thickness overthe entire substrate surface are from 29.5 nm to 55.2 nm, from 90.5 nmto 109.5 nm, from 151.6 nm to 164.8 nm, and the like. Variations in thedegree of crystallization caused by variations in the film thicknesswithin the substrate surface can be reduced provided that lasercrystallization of the entire substrate surface is performed by usingthe second harmonic (532 nm) of a CW Nd:YVO₄ laser with the filmthickness of the a-Si film set to one of the above ranges for the laserirradiation process.

Once the set film thickness of the a-Si film is determined, the a-Sifilm may then be formed with the determined film thickness on the glasssubstrate if laser crystallization of the a-Si film substrate is to beperformed by using the second harmonic (532 nm) of a CW Nd:YVO₄ laser.

Further, even if the set film thickness is not achieved during formationof the a-Si film, additional film formation or film reduction by etchingmay be conducted to achieve the set film thickness for the laserirradiation process.

For cases in which crystallization over the entire substrate surface isnot necessary, and for cases in which it is not necessary to reducevariations in the degree of crystallization over the entire substratesurface, the range to which the film thickness is measured may belimited to portions of the substrate where it is desired to reducevariations in the degree of crystallization.

Embodiments Embodiment 1

A method of manufacturing a TFT in which variation in the TFTcharacteristics within the surface of a substrate are reduced isdiscussed as Embodiment 1. For cases in which a continuous grain silicon(poly-Si) film, formed on a glass substrate having an insulating film,is crystallized over the entire surface of the substrate by using thesecond harmonic (532 nm) of a pulse Nd:YAG laser, variations in the filmthickness of the poly-Si film depending on locations within thesubstrate surface, and the poly-Si film thickness dependence of theabsorptivity of 532 nm light are investigated in advance, before lasercrystallization processing. The film thickness of the irradiation filmis set so that variations in the degree of crystallization within thesubstrate surface after performing laser crystallization therein arereduced and thereafter, laser crystallization is performed.

In Embodiment 1, the irradiation film is taken as poly-Si film obtainedby solid phase crystallization (SPC) of a-Si film formed by plasmachemical vapor deposition (CVD). Further, the absorptivity of 532 nmlight by the poly-Si film substrate is taken as A(t) within Embodiment1, where t is denotes the poly-Si film thickness.

Variations in the film thickness of the poly-Si film, and the dependenceof the absorptivity of 532 nm light on the poly-Si film thickness areinvestigated before forming the a-Si film. Film formation of an a-Sifilm on a dummy substrate having the same size as the actual substratemay be performed, for example, and the film thickness may be measured atmany points within the surface of the dummy substrate by using anellipsometer in order to investigate film thickness variations. Althoughan SPC method is used in making the a-Si film into a poly-Si film, thefilm thickness does not vary during phase changes from the a-Si film tothe poly-Si film, and therefore the film thickness data measured at manypoints within the substrate surface may also be treated as poly-Si filmdata. A substrate on which a poly-Si film is formed, and the filmthickness of the poly-Si film is already known, may be used to makeactual absorptivity measurements by using a spectrophotometer, forexample, in order to investigate the dependence of the absorptivity of532 nm light on the poly-Si film thickness. Alternatively, the filmthickness of the poly-Si film and its index of refraction may bemeasured by using an ellipsometer, and the light absorptivity A(t) maybe simulated. The latter method does not entail much trouble, and isuseful in understanding how the light absorptivity continuously dependson the film thickness.

The film thickness distribution of the poly-Si film within the surfaceof the substrate becomes ±5%, similar to the variations in filmthickness of the a-Si film within the surface of the substrate discussedin the Embodiment Mode. It can thus be seen that there will bevariations in film thickness within the substrate surface of a maximumfilm thickness equal to 1.05 t, and a minimum film thickness equal to0.95 t, if the target film thickness for poly-Si film formation is takenas t.

Refer to FIGS. 4A and 4B. In FIG. 4A, reference numeral 401 denotes alight absorptivity A(t) at 532 nm found by a computer simulationperformed based on an index of refractive index (n) and an extinctionconstant (k) obtained from an ellipsometer. Reference numeral 402denotes a derivative dA(t)/dt of the light absorptivity A(t), andreference numeral 403 denotes actual measured values of lightabsorptivity at 532 nm when varying the poly-Si film thickness. Notethat, for convenience of computation, the difference between thevariations in the light absorptivity with respect to the film thicknessmay be found as a substitute for the derivative of the lightabsorptivity A(t).

By comparing the actual measured values 403 with the simulation 401, itcan be seen that, although there is a small difference with the lightabsorptivity itself, the values of the poly-Si film thickness at whichlight absorptivity at 532 nm takes the maximum value and the minimumvalue have relatively good agreement. However, the values found here donot agree with the values of the a-Si film thickness, discussed inEmbodiment 1, at which light absorptivity at 532 nm takes the maximumand minimum values.

If the derivative dA(t)/dt of the light absorptivity is found from thesimulation results of the light absorptivity at 532 nm by the a-Si film,and poly-Si film thickness ranges in which dA(t)/dt>0 are selected, thena range from 1 nm to 9 nm, a range from 33 nm to 63 nm, a range from 91nm to 123 nm, a range from 155 nm to 185 nm, and the like are found.Variations in the degree of crystallization due to film thicknessvariations can be reduced in a self-alignment manner, provided that thefilm thickness of the poly-Si film is within these ranges. This can beclearly understood by referring to FIG. 4B in which the graph of a 20 nmto 90 nm region of FIG. 4A is blown up.

The poly-Si film formed on the glass substrate at a target filmthickness of t possesses film thickness variations within the substratesurface, with the maximum film thickness equal to 1.05 t and the minimumfilm thickness equal to 0.95 t. Therefore the film thickness t may beselected so that dA(t)/dt>0 is always achieved, even if the filmthickness fluctuates from 0.95 t to 1.05 t, in order to reducevariations in the degree of crystallization, due to film thicknessvariations over the entire substrate surface, in a self-alignmentmanner.

It can thus be seen from the above method that the target film thicknessof a poly-Si film capable of reducing variations in the degree ofcrystallization, due to dispersions in the film thickness over theentire substrate surface in a self-alignment manner, is from 1.1 nm to8.6 nm, from 31.4 nm to 60.0 nm, from 95.8 nm to 117.1 nm, from 163.2 nmto 176.2 nm, and the like. Variations in the degree of crystallizationcaused by dispersions in the film thickness within the substrate surfacecan be reduced provided that laser crystallization of the entiresubstrate surface is performed by using the second harmonic (532 nm) ofa CW Nd:YVO₄ laser with the film thickness of the poly-Si film set toone of the above ranges for the laser irradiation process.

Once the set film thickness of the poly-Si film is determined, thepoly-Si film may then be formed at the determined film thickness on theglass substrate if laser crystallization of the poly-Si film substrateis to be performed by using the second harmonic (532 nm) of a CW Nd:YVO₄laser.

For cases in which crystallization over the entire substrate surface isnot necessary, and for cases in which it is not necessary to reducevariations in the degree of crystallization over the entire substratesurface, the range of the poly-Si film to which the film thickness ismeasured may also be limited to portions of the substrate where it isdesired to reduce variations in the degree of crystallization.

Variations in the degree of crystallization during laser crystallizationcan be reduced by the laser beam irradiation method of the presentinvention, even for cases in which there are film thickness variationswithin the surface of a non-single crystal semiconductor.

1. A laser beam irradiation method comprising: obtaining data showing adependence of a light absorptivity upon a film thickness of asemiconductor film at a certain wavelength of a laser beam; forming asemiconductor film having a film thickness distribution over asubstrate; and irradiating the semiconductor film with a laser beam tocrystallize the semiconductor film, wherein a differential coefficientof an absorptivity of the laser beam with respect to a film thickness ofthe semiconductor film is positive.
 2. A laser beam irradiation methodaccording to claim 1, wherein the laser beam is a pulse oscillationlaser beam.
 3. A laser beam irradiation method according to claim 2,wherein the pulse oscillation laser beam comprises a high harmonic of asolid pulse laser.
 4. A laser beam irradiation method according to claim3, wherein the laser beam comprising the high harmonic of the solidpulse laser is one selected from the group consisting of an Nd:YAG laserbeam, an Nd:YVO₄ laser beam, and an Nd:YLF laser beam.
 5. A laser beamirradiation method according to claim 1, wherein the laser beam is acontinuous wave laser beam.
 6. A laser beam irradiation method accordingto claim 5, wherein the continuous wave laser beam is an Ar laser beam.7. A laser beam irradiation method according to claim 5, wherein thecontinuous wave laser beam comprises a high harmonic of a solidcontinuous wave laser.
 8. A laser beam irradiation method according toclaim 7, wherein the laser beam comprising the high harmonic of thesolid continuous wave laser is one selected from the group consisting ofan Nd:YAG laser and an Nd:YVO₄ laser.
 9. A laser beam irradiation methodaccording to claim 1, wherein the certain wavelength of the laser beamis 532 nm.
 10. A laser beam irradiation method according to claim 1,wherein the data are obtained by a computer simulation.
 11. A laser beamirradiation method comprising: obtaining data showing a dependence of alight absorptivity upon a film thickness of a first semiconductor filmat a certain wavelength of a laser beam; after obtaining the dataforming a second semiconductor film having a film thickness distributionover a substrate; and irradiating the second semiconductor film with alaser beam to crystallize the second semiconductor film, wherein thefilm thickness of the second semiconductor film is determined by arefractive index of the first semiconductor film at the certainwavelength of the laser beam.
 12. A laser beam irradiation methodaccording to claim 11, wherein the laser beam is a pulse oscillationlaser beam.
 13. A laser beam irradiation method according to claim 12,wherein the pulse oscillation laser beam comprises a high harmonic of asolid pulse laser.
 14. A laser beam irradiation method according toclaim 13, wherein the laser beam comprising the high harmonic of thesolid pulse laser is one selected from the group consisting of an Nd:YAGlaser beam, an Nd:YVO₄ laser beam, and an Nd:YLF laser beam.
 15. A laserbeam irradiation method according to claim 11, wherein the laser beam isa continuous wave laser beam.
 16. A laser beam irradiation methodaccording to claim 15, wherein the continuous wave laser beam is an Arlaser beam.
 17. A laser beam irradiation method according to claim 15,wherein the continuous wave laser beam comprises a high harmonic of asolid continuous wave laser.
 18. A laser beam irradiation methodaccording to claim 17, wherein the laser beam comprising the highharmonic of the solid continuous wave laser is one selected from thegroup consisting of an Nd:YAG laser and an Nd:YVO₄ laser.
 19. A laserirradiation method according to claim 11, wherein the certain wavelengthof the laser beam is 532 nm.
 20. A laser beam irradiation methodaccording to claim 11, wherein the data are obtained by a computersimulation.
 21. A method of manufacturing a thin film transistorcomprising: obtaining data showing a dependence of a light absorptivityupon a film thickness of a semiconductor film at a certain wavelength ofa laser beam; forming a semiconductor film having a film thicknessdistribution over a substrate; and irradiating the semiconductor filmwith a laser beam to crystallize the semiconductor film, wherein adifferential coefficient of an absorptivity of the laser beam withrespect to a film thickness of the semiconductor film is positive.
 22. Amethod of manufacturing a thin film transistor according to claim 21,wherein the laser beam is a pulse oscillation laser beam.
 23. A methodof manufacturing a thin film transistor according to claim 22, whereinthe pulse oscillation laser beam comprises a high harmonic of a solidpulse laser.
 24. A method of manufacturing a thin film transistoraccording to claim 23, wherein the laser beam comprising the highharmonic of the solid pulse laser is one selected from the groupconsisting of an Nd:YAG laser beam, an Nd:YVO₄ laser beam, and an Nd:YLFlaser beam.
 25. A method of manufacturing a thin film transistoraccording to claim 21, wherein the laser beam is a continuous wave laserbeam.
 26. A method of manufacturing a thin film transistor according toclaim 25, wherein the continuous wave laser beam is an Ar laser beam.27. A method of manufacturing a thin film transistor according to claim25, wherein the continuous wave laser beam comprises a high harmonic ofa solid continuous wave laser.
 28. A method of manufacturing a thin filmtransistor according to claim 27, wherein the laser beam comprising thehigh harmonic of the solid continuous wave laser is one selected fromthe group consisting of an Nd:YAG laser and an Nd:YVO₄ laser.
 29. Amethod of manufacturing a thin film transistor according to claim 21,wherein the certain wavelength of the laser beam is 532 nm.
 30. A methodof manufacturing a thin film transistor according to claim 21, whereinthe data are obtained by a computer simulation.
 31. A method ofmanufacturing a thin film transistor comprising: obtaining data showinga dependence of a light absorptivity upon a film thickness of a firstsemiconductor film at a certain wavelength of a laser beam; afterobtaining the data forming a second semiconductor film having a filmthickness distribution over a substrate; and irradiating the secondsemiconductor film with a laser beam to crystallize the secondsemiconductor film, wherein the film thickness of the secondsemiconductor film is determined by a refractive index of the firstsemiconductor film at the certain wavelength of the laser beam.
 32. Amethod of manufacturing a thin film transistor according to claim 31,wherein the laser beam is a pulse oscillation laser beam.
 33. A methodof manufacturing a thin film transistor according to claim 32, whereinthe pulse oscillation laser beam comprises a high harmonic of a solidpulse laser.
 34. A method of manufacturing a thin film transistoraccording to claim 33, wherein the laser beam comprising the highharmonic of the solid pulse laser is one selected from the groupconsisting of an Nd:YAG laser beam, an Nd:YVO₄ laser beam, and an Nd:YLFlaser beam.
 35. A method of manufacturing a thin film transistoraccording to claim 31, wherein the laser beam is a continuous wave laserbeam.
 36. A method of manufacturing a thin film transistor according toclaim 35, wherein the continuous wave laser beam is an Ar laser beam.37. A method of manufacturing a thin film transistor according to claim35, wherein the continuous wave laser beam comprises a high harmonic ofa solid continuous wave laser.
 38. A method of manufacturing a thin filmtransistor according to claim 37, wherein the laser beam comprising thehigh harmonic of the solid continuous wave laser is one selected fromthe group consisting of an Nd:YAG laser and an Nd:YVO₄ laser.
 39. Amethod of manufacturing a thin film transistor according to claim 31,wherein the certain wavelength of the laser beam is 532 nm.
 40. A methodof manufacturing a thin film transistor according to claim 31, whereinthe data are obtained by a computer simulation.
 41. A method ofmanufacturing a semiconductor device having a pixel portion and adriving circuit comprising the steps of: obtaining data showing adependence of a light absorptivity upon a film thickness of asemiconductor film at a certain wavelength of a laser beam; forming asemiconductor film having a film thickness distribution over asubstrate; and irradiating the semiconductor film with a laser beam tocrystallize the semiconductor film, wherein a differential coefficientof an absorptivity of the laser beam with respect to a film thickness ofthe semiconductor film is positive.
 42. A method of manufacturing asemiconductor device according to claim 41, wherein the semiconductordevice is an active matrix type display device.
 43. A method ofmanufacturing a semiconductor device according to claim 41, wherein thelaser beam is a pulse oscillation laser beam.
 44. A method ofmanufacturing a semiconductor device according to claim 41, wherein thepulse oscillation laser beam comprises a high harmonic of a solid pulselaser.
 45. A method of manufacturing a semiconductor device according toclaim 41, wherein the laser beam comprising the high harmonic of thesolid pulse laser is one selected from the group consisting of an Nd:YAGlaser beam, an Nd:YVO₄ laser beam, and an Nd:YLF laser beam.
 46. Amethod of manufacturing a semiconductor device according to claim 41,wherein the laser beam is a continuous wave laser beam.
 47. A method ofmanufacturing a semiconductor device according to claim 41, wherein thecontinuous wave laser beam is an Ar laser beam.
 48. A method ofmanufacturing a semiconductor device according to claim 41, wherein thecontinuous wave laser beam comprises a high harmonic of a solidcontinuous wave laser.
 49. A method of manufacturing a semiconductordevice according to claim 41, wherein the laser beam comprising the highharmonic of the solid continuous wave laser is one selected from thegroup consisting of an Nd:YAG laser and an Nd:YVO₄ laser.
 50. A methodof manufacturing a semiconductor device according to claim 41, wherein awavelength of the laser beam is greater than 350 nm.
 51. A method ofmanufacturing a semiconductor device according to claim 41, wherein thecertain wavelength of the laser beam is 532 nm.
 52. A method ofmanufacturing a semiconductor device according to claim 41, wherein thedata are obtained by a computer simulation.
 53. A method ofmanufacturing a semiconductor device having a pixel portion and drivingcircuit comprising the steps of: obtaining data showing a dependence ofa light absorptivity upon a film thickness of a first semiconductor filmat a certain wavelength of a laser beam; after obtaining the dataforming a second semiconductor film having a film thickness distributionover a substrate; and irradiating the second semiconductor film with alaser beam to crystallize the second semiconductor film, wherein thefilm thickness of the second semiconductor film is determined by arefractive index of the first semiconductor film at the certainwavelength of the laser beam.
 54. A method of manufacturing asemiconductor device according to claim 53, wherein the semiconductordevice is an active matrix type liquid crystal display device.
 55. Amethod of manufacturing a semiconductor device according to claim 53,wherein the laser beam is a pulse oscillation laser beam.
 56. A methodof manufacturing a semiconductor device according to claim 53, whereinthe pulse oscillation laser beam comprises a high harmonic of a solidpulse laser.
 57. A method of manufacturing a semiconductor deviceaccording to claim 53, wherein the laser beam comprising the highharmonic of the solid pulse laser is one selected from the groupconsisting of an Nd:YAG laser beam, an Nd:YVO₄ laser beam, and an Nd:YLFlaser beam.
 58. A method of manufacturing a semiconductor deviceaccording to claim 53, wherein the laser beam is a continuous wave laserbeam.
 59. A method of manufacturing a semiconductor device according toclaim 53, wherein the continuous wave laser beam is an Ar laser beam.60. A method of manufacturing a semiconductor device according to claim53, wherein the continuous wave laser beam comprises a high harmonic ofa solid continuous wave laser.
 61. A method of manufacturing asemiconductor device according to claim 53, wherein the laser beamcomprising the high harmonic of the solid continuous wave laser is oneselected from the group consisting of an Nd:YAG laser and an Nd:YVO₄laser.
 62. A method of manufacturing a semiconductor device according toclaim 53, wherein the certain wavelength of the laser beam is 532 nm.63. A method of manufacturing a semiconductor device according to claim53, wherein the data are obtained by a computer simulation.
 64. A methodof manufacturing a semiconductor device according to claim 53, wherein awavelength of the laser beam is greater than 350 nm.